SOLUTION: What is the reasoning behind the division of fractions? For example, what does it mean to divide 1/2 by 2/3? Note: I'm not looking for the algorithm or the rule for generating the

Question 305634: What is the reasoning behind the division of fractions? For example, what does it mean to divide 1/2 by 2/3? Note: I'm not looking for the algorithm or the rule for generating the correct answer but rather the explanation of what it means.
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
Well let's take a slightly different problem that can be easily expressed in decimal format.
1/2 divided by 3/4
.50/.75
multiply by 100
50/75
factor out 25
2/3
What just happened.
We want to know how many times 3/4 can go into 1/2
Well it can't go a complete time because 3/4 is larger than 1/2
the ratio holds true for 50/75
How many times can 75 go into 50 it can't one whole time. It can go 2/3 of 1 time?
But what is interesting to me about this problem and yours is how we resolve the problem using fractions.
(1/2)/(2/3)=1/2*3/2=/3/4
and
(1/2) /(3/4) = 1/2*4/3=4/6=2/3 as we learned before.
We used the reciprocals to multiply rather than divide.

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